Seattle's monorail: a vision of the future … in 1962. Photograph: Raimund Koch/Corbis

My recent, first trip to London presented me with two surprises: the reach, convenience, and frequency of the tube, and the volume of Londoners' complaints about the reach, convenience, and frequency of the tube.

English friends had explained to me, not without pride, the importance of grumbling to the national character, but I still want to stress to every Londoner I meet that — take it from a visiting Los Angeleno — the tube exists, and that counts as no trifling achievement. Beyond that, and like every other means of urban transport system around the world, it tells you nearly everything you need to know about the city it serves.

If you wish to understand London or any place else, look no further than how people move through it. This goes not just for subways, but overground trains, buses, cycleways, rickshaws, and every mobility solution in between. You can learn a great deal from robust transport systems, and even more from underdeveloped ones.

This line of thinking never occurred to me in my years growing up just outside Seattle, a city which I frequented but never gave much thought. Seattle's "retro-futuristic" image has, for the past half century, rested in large part on a pair of structures built for its 1962 World's Fair: the globally recognisable Space Needle, and the lesser-known but still sadly evocative monorail. While neither offer much of everyday value to the locals, the monorail – which takes the form but, in running back and forth on only a mile of track, not the function of a dedicated public transit system – stands as a reminder of the city's many frustrated attempts at complete urbanisation. Proposals for a useful monorail network have risen and fallen over the years; the first light rail line there opened only in 2009.

The surprisingly backward state of Seattle transport tells a story familiar to many American cities: an aesthetically bold, forward-looking optimism in the years after the second world war, followed by decades of bitter struggle with its own demanding suburbs, home in this case to the mighty or once-mighty likes of Boeing and Microsoft. Amazon's recent relocation of its offices to downtown Seattle bodes well for the life of the city proper, but it still has no end of catching up to do with the metropolises of Europe, Asia and Latin America, where high densities of transit not only exist, but make statements about the cities that built them.

Often the style of a city's transport reflects how that city sees itself, or would like to. The still-gleaming Santiago metro opened in 1975 as a declaration of Chile's emergence, real or desired, from provincial isolation. With improvements that have turned it over the past 25 years into South America's most extensive subway, it also announces the country's escape from dictatorship. "Make sure you ride the metro," Santiaguinos abroad would insist to me upon hearing of my plans to visit their city.

Despite the grumbles from its passengers, the tube functions as London's main arteries. Photograph: Stefan Wermuth/Reuters

Few outside Chile know the high quality of Santiago's transport, but everyone knows the high quality of Tokyo's. Before making my first trip to Japan, I prepared myself for astonishment at the functionality of its trains. I also prepared myself for the white-gloved hands of the oshiya, or "pushers" – station workers employed to cram as many rush-hour commuters as possible behind a subway car's closing doors. In the event, though I never felt the touch of the oshiya, I was impressed not just at the perfectly punctual, all-reaching trains, but the way riders regard them not as objects of great municipal and national pride, but as expected necessities.

Japanese major cities, more than any others of my acquaintance, run on expectations – a constant stream of them, routinely fulfilled to the slightest detail. If the schedule says the bus will show up at 8:31, a Kyoto-based English friend told me, people start looking at their watches at 8:32. Even in Osaka, Japan's comparatively Falstaffian second city, reputedly characterised by rustic straightforwardness and saturated with vulgar capitalist energy, the trains (on which I never saw anyone drink, eat, or speak into a mobile phone) adhere to a standard of regularity no less rigorous than Tokyo's.

Korea, with less time to develop than Japan and more development to do, has given rise in Seoul to a city that appears to have only just been torn out of its packaging. None of its 50 tallest towers have stood for even 30 years, and most of the Seoul metropolitan subway that takes you between them entered service more recently than that. The longest (and busiest, and most station-equipped) such system in the world has developed into not just a means of getting efficiently from Apgujeong to Bokjeong, but a showcase of the spirit that turned a city in shambles in the 1960s into a vision even the most space age-minded American of that era wouldn't have entertained.

But for everyone who sees the future in Seoul or Tokyo, many more see it, with hope or regret, in Shanghai. The astonishing speed with which infrastructure has sprouted in the Chinese city inspires contradictory feelings in those of us based in slower-growing cities: envy that our governments can't build whole rapid transit systems in a matter of years, tempered by relief that they lack the authority necessary to do so. Ride a train in a Chinese metropolis and, by all accounts, you experience the idea of cities as massive logistical problems; object lessons that even the ambition and resources that China commands can't alone solve them.

Los Angeles attained its vast size and bizarre shape due to the growth of its first, early 20th-century, pre-population-boom rail system, the formidable "red cars" and "yellow cars" of the Pacific Electric and Los Angeles Railroads. But the sweeping eight-lane freeways that replaced them after the war still monumentalise the freedom of speed and impulsive mobility – at least when you drive on them in the middle of the night.

A jeepney in Manila: US military 4x4s left over from world war II have been converted, often flamboyantly, into the most popular form of transport in the city. Photograph: Thom Lang/Corbis

One of its components actually began in 1900 as a six-mile bicycle highway, an innovation that sounds more suited to modern Copenhagen than to LA in any era. Because the Danish capital has spent the past half-century encouraging cycling as a primary means of transport, you'll learn far less about the city on its limited, expensive subway than you will on its wide, traffic-separated bicycle lanes, observing the cross-section of the population that pedals all around you. Of all Copenhagen's sights, none blows American minds more than that of one of the city's many girls in skirt and spike heels, cigarette in one hand, mobile phone in the other — sitting on, of all things, a bicycle.

As it has elevated "hygge" (cosiness) into a way of life, Copenhagen has elevated the humble bicycle into a cultural icon, a pillar of its image. London has done the same with black taxis and doubledecker buses – not to mention "mind the gap" as a take-away phrase for tourists, expats and students. But while New York's cabs exude a trademark rough-edged urbanity, American cities don't usually represent themselves with elements of transit – apart, that is, from the classic yellow school bus.

Regular American city buses are typically maligned, due to the supposed poverty of their riders. This gearing of public transport toward the socioeconomic margins, especially margins seen as isolated from or in conflict with the majority, impedes popularity and thus implementation; dedicating a bus lane in Los Angeles has proven a task comparable to the labours of Hercules.

The bicycle in America has only just begun to escape similar associations. Most designations of bike-friendliness have gone not to proper cities but college towns: Davis, Boulder, Long Beach, Iowa City – places that, while pleasant enough, command little national, let alone international import. Modest Portland, Oregon, the US city in which I most enjoy cycling, feels like a Tokyo or Seoul by comparison. Yet despite its reputation as a paradise for alternative transport, I always notice suspiciously few normally clothed riders on the road there with me. Ride a bike in any of America's supposedly top cities to do so, and you come to know the still-strong American genius for branding, as opposed to the faltering American genius for execution. When Los Angeles laid down its first high-profile cycle lane, the rain washed it mostly away within months.

Even as a city's forms of transport empower us, they limit us, reducing us to a narrow set of obsessions: New Yorkers' compulsive but futile questions about when the train will come; Angelenos' sad, Sisyphean quest for free parking; Copenhageners' budgeting for their next bicycle when their current one inevitably gets stolen; Londoners' ceaseless insistence that the whole of their infrastructure lies more or less in ruins. Yet they can also make manifest the human ingenuity that makes such improbable accretions as cities work in the first place.

A Filipino friend once described Manila to me as a transport enthusiast's paradise, albeit one made up of many thousands of small, barely-maintained units. Anyone who boards a "jeepney" (a US Army jeep, flamboyantly converted for public transportation) there gains insight into the culture of repurposing and improvisation that keeps the city chugging along, whichever natural, political, or infrastructural disasters may come. You get the same sense from a ride on one of Mexico City's green "pesero" microbuses – icons, too, in their way – which pick up and drop off passengers where required, rather than on a set route.

Certain developing cities have drawn the eyes of the rest of the urban world with their transport alone: Curitiba in Brazil, made its name by pioneering bus-based rapid transit, a form of which, over in the Colombian capital, Bogotá, has also made a hearty go. Enrique Peñalosa, Bogotá's former mayor, has proven eminently quotable on the matter of transport as a reflection of metropolitan character and building the means of transport as a way of defining that character. "An advanced city," he has proclaimed, "is not a place where the poor move about in cars; rather, it's where even the rich use public transportation."

This goes a fair way to explaining the seething frustrations of many American cities, composed in large part of poor people in cars, made ever poorer by their associated costs. Peñalosa has also spoken of our "need to walk, just as birds need to fly", suggesting a city's need for "pedestrian infrastructure shows respect for human dignity". And indeed, you can learn as much about a city from observing how people walk in it as how they ride, cycle, and drive. I did so in London, whose citizens cross the street any time they please, regardless of what the traffic signal says. Me and my Los Angeles compatriots remain, alas, too cowed by the pricey threat of jaywalking tickets, the monstrously aggressive (and in my experience mythical) spectre of the "LA driver", and the sheer width of the roads to do the same.

We can learn from London, I told myself, and the thought cheered me. It had to, as I'd wound up stranded by the tube strike, an illuminating transport phenomenon which had me revising my opinions about the city all over again. We can learn from London, yes, but let's not learn everything from it.